Answers

That is called 関西弁(Kansai dialect). The situation of saying やったろうやんけ is like there is almost no possibility that you can do, or you can beat, but still, you want to believe that you can beat it.

ex; Baseball scores 4-1, the B team, which has got 1 point, is in hell now. Other teammates are almost giving up, but one player still believe that there is a possibility to win. Then he'll say like やったろうやんけ!! meaning "we'll show 'em what we've got!!" Or, scores 4-4, and say "I'll hit a game-winning RBI!!"

The way to use やったろうやんけ is like that. I don't really know about baseball rules, besides, I'm not from Kansai... :P Anyway, that's very casual way to say.